In this task, you will be presented with a context from an academic paper and a question separated with a 
. You have to answer the question based on the context.

[Q]: Combining the modulus part and the phase part, HAKE maps entities into the polar coordinate system, where the radial coordinate and the angular coordinates correspond to the modulus part and the phase part, respectively. 
 Question: How are entities mapped onto polar coordinate system?
[A]: radial coordinate and the angular coordinates correspond to the modulus part and the phase part, respectively


[Q]: Contextualized word embeddings, sentence embeddings, such as deep contextualized word representations BIBREF20 , BERT BIBREF22 , encode the complex characteristics and meanings of words in various context by jointly training a bidirectional language model.  The second method is to use sentence embeddings, BERT. It is used to a generate single 786-dimensional sentence embedding from 10k-dimensional one-hot vector or distribution over previous words and then merge into a single context vector with two different merging methods. Using this approach, we can obtain a more dense, informative, fixed-length vectors to encode conversational-context information, $e^k_{context}$ to be used in next $k$ -th utterance prediction. We use contextual gating mechanism in our decoder network to combine the conversational-context embeddings with speech and word embeddings effectively. Our gating is contextual in the sense that multiple embeddings compute a gate value that is dependent on the context of multiple utterances that occur in a conversation.  Let $e_w = e_w(y_{u-1})$ be our previous word embedding for a word $y_{u-1}$ , and let $e_s = e_s(x^k_{1:T})$ be a speech embedding for the acoustic features of current $k$ -th utterance $x^k_{1:T}$ and $e_c = e_c(s_{k-1-n:k-1})$ be our conversational-context embedding for $n$ -number of preceding utterances ${s_{k-1-n:k-1}}$ . Then using a gating mechanism:

$$g = \sigma (e_c, e_w, e_s)$$ (Eq. 15)

where $\sigma $ is a 1 hidden layer DNN with $\texttt {sigmoid}$ activation, the gated embedding $e$ is calcuated as

$$e = g \odot (e_c, e_w, e_s) \\ h = \text{LSTM}(e)$$ (Eq. 16)

and fed into the LSTM decoder hidden layer.  The output of the decoder $h$ is then combined with conversational-context embedding $e_c$ again with a gating mechanism,

$$g = \sigma (e_C, h) \\ \hat{h} = g \odot (e_c, h)$$ (Eq. 17)

Then the next hidden layer takes these gated activations, $\hat{h}$ , and so on. 
 Question: How are sentence embeddings incorporated into the speech recognition system?
[A]: BERT generates sentence embeddings that represent words in context. These sentence embeddings are merged into a single conversational-context vector that is used to calculate a gated embedding and is later combined with the output of the decoder h to provide the gated activations for the next hidden layer.


[Q]: word embedding, input encoder, alignment, aggregation, and prediction 
 Question: what is the architecture of the baseline model?
[A]:
word embedding, input encoder, alignment, aggregation, and prediction.


